3.5.1 Database
We applied the proposed method to three different CT datasets including nor-mal/abnormal data, Arterial (ART) /Portal venous (PV)/ Delay (DL) phases data. The first dataset included 26 CT images of the abdominal region records with a resolution of 0.683×0.683×1mm3 and a size of 512×512×(159-263) pixels.
We call Group-I in this work. Group-I was acquired from normal and pathological cases of patients between 20 and 75 years old. The samples contained 20 normal cases and 6 pathological cases: from No.1 to No.20 were normal cases and from No.21 to No.26 belonged to pathological cases. Therein, patients (pathological cases) were those who were suspected of having a disease, such as chronic liver dis-ease, and were scanned in the course of diagnosis. The second dataset contained 7 abnormal data of phase-ART records with a resolution of 0.683×0.683×1.25mm3 and a size of 512×512×(191-365) pixels. We called it Group-II (High-resolution) in this work. The third dataset included 23 data records with a resolution of 2.479×2.479 ×5.382mm3 and a size of 128×128×36 pixels. We call Group-III (Low-resolution) in this work. In order to make a quantitative evaluation for our proposed method, the liver was segmented for each image (i.e., subject) manually as the ground truth. The segmentation was performed under the guidance of a physician in order to obtain accurate liver volumes. This work was conducted with the approval of the institutional review boards at University Ethics Committee, and all data provided written informed consent.
The proposed algorithm was implemented in a MS-Windows-based personal computer (IntelRCoreTM-i7 3770QM 3.40GHz and 16GB-DRAM). The
program-Algorithm 1 RWNBT Algorithm for Multi-organ Segmentation
ObjectSeed(OS); BackgroundSeed(BS); IntensityConstraint(IC); ShapeCon-straint(SC);
Preprocessing:
Step 1: Extract the abdomen region from the raw CT data;
Step 2: Manually select two start slices in the axial plane and define the object-s/background seeds on them: the largest spleen is the first start slice and the largest liver is the second start slice;
Mainprocessing:
Step 3: Estimate the initial intensity model on the first start slice using GM, then generate the thresholded image;
Step 4: Segment two organs in the thresholded image for the first start slice using RW;
Step 5: Obtain the IC and SC based on the segmented organs in the first start slice;
for all the lower slices, starting from the first start slicedo
Step 6: Estimate the GMM model of two organ’s intensity based on IC, then generating the thresholded image;
Step 7: Select the rough OS/BS based on SC;
Step 8: Select the fine OS/BS using NBT;
Step 9: Perform slice segmentation on the thresholded image using RW;
Step 10: Add the segmentation results of this slice to the output volume;
Step 11: Update the IC and SC based on the segmentation results of the current slice;
end for
Step 12: Estimate the initial intensity model on the second start slice using GM, then generate the thresholded image;
Step 13: Segment two organs in the thresholded image for the second start slice using RW;
Step 14: Update the IC and SC based on the segmented organs in the second start slice;
for all the intrazonal slices, between the second start slice and the first start slice do
Repeat Step 6–Step 11;
end for
Step15: Updating the IC and SC based on the segmented organs in the second start slice;
for all the upper slices, starting from the second start slicedo Repeat Step 6–Step 11;
end for
Step16: Smoothing the boundary of the segmented volume using FT;
ming environment was coded in the MATLAB environment. Visualization of the shapes was performed using VTK [19], written in the C++ language.
3.5.2 Quantitative Measurement
To measure the accuracy of our method, we compared it with the conventional RW method and the state-of-the-art interactive segmentation algorithms using two metrics.
Dice Coefficient (Dice) The Dice coefficient is one of the most popular meth-ods to evaluate segmentation accuracy. This metric is given in percent and based on the voxels of two binary 3D volumes, with Vmanual as the manually and Vauto as the automatically segmented organ.
Dice= 2|Vmanual∩Vauto|
|Vmanual|+|Vauto| ×100% (3.15)
Volumetric Overlap Error (VOE) The volumetric overlap error between two sets of voxels Vmanual and Vauto is given in percent. This ratio is also known as Tanimoto or Jaccard coefficient.
V OE = |Vmanual∩Vauto|
|Vmanual∪Vauto| ×100% (3.16)
3.5.3 Single-Organ Segmentation Results
A. Quantitative Validation of Single-Organ Segmentation
To investigate the performance of our proposed segmentation method, we applied our proposed RWNBT method to Group-I dataset. The segmentation results of two typical cases are shown in Fig. 3.6. The results in Fig. 3.6 proved that per-forming the RWNBT method to segment the livers can give us accurate results. A common difficulty for computer-aided liver segmentation is the erroneous inclusion of heart volumes, which our method robustly avoided. It confirmed the ability of our method to segment the livers with a precision segmentation result.
Additional challenges come from enlarged livers, where the liver has large shape variations which made it very difficult to be segmented. Taking this limitation into consideration, in this research, our technique performed on 26 CT scans that combined normal cases and pathological cases with large morphological variations.
Fig. 3.6 shows the liver segmentation result from one pathological case. It proved the performance of our proposed algorithm which was robust for segmenting the liver in the pathological cases with large morphological variations.
Figure 3.6: Comparison of the manual segmentation (blue) with the segmentation results of our method (red). The first row is the segmentation result in Case 9. The second row is the segmentation result in Case 16. The third row is the segmentation result of pathological case with unusual liver shape in Case 21.
Figure 3.7: Our technique performed on the Group-I dataset with Dice measure-ment. The first 20 data is normal cases and the remaining 5 data is pathological cases.
Apart from a visual inspection, a quantitative evaluation was conducted. Fig. 3.7 gave a more clear depiction of the corresponding accurate results of 26 cases. The first 20 data corresponds to normal cases (the average Dice is 0.951) and the re-maining 5 data is pathological cases (the average Dice is 0.941). Regarding the result of applying our method to synthetic shapes, we can conclude that our pro-posed method was robust in addressing the segmentation of the liver (with the average Dice’s similarity coefficient = 0.949). Future research directions will in-clude applying our method on more datasets in order to more accurately evaluate the performance.
B. Qualitative Comparison of Single-Organ Segmentation
To evaluate the effectiveness of the proposed method (RWNBT), RWNBT was compared with the classical Random Walks (RW3D) [8]. Considering the memory usage demands for applying the RW3D algorithm to the computer, we resized all of our dataset (512×512×(159−263) pixels) into the size of 128×128×36 pixels.
Computation time is an important metric for evaluating one segmentation al-gorithm. For the classical RW algorithm, the basis of RW method is a large, sparsely occupied linear equations, whose size corresponds to the number of vox-els in the 3D medical image. Hence, it exhibited slowness for solving 3D image segmentation. In order to assess the potential benefits of our proposed method, one typical clinical CT case in our dataset was randomly chosen to perform the RWNBT and RW3D method for liver segmentation. After extracting the bound-ing box of abdomen, this data was resized into the size of 126×86×33 pixels.
Tests were performed on this data with the different number of slices to illustrate the computational burden for the classical RW3D algorithm. To more accurately
compare the segmentation runtime and accuracy, we defined the seeds with a fixed number on the same slice.
Fig. 3.8 shows the comparison of the Dice similarity coefficient and the runtime in seconds between the our proposed RWNBT method and the classical random walks with 3D graph (RW3D). We can observe that the computation time of R-WNBT would be closer to a linear increase corresponding to an increase in the image size, while the computation time of RW3D shows an exponential growth with the size of image. This may be explained by considering a slice-by-slice man-ner was applied to automatically segment the liver for the whole volume in our method. A significant reduction in runtime values using RWNBT based segmen-tation compared with those based on RW3D was confirmed.
In addition, it reveals that Dice value remains relatively stable with an increase in the image size using our RWNBT method. Meanwhile, the Dice curve of the RW3D method falls in a downward trend. Since with the increase of the image size, a higher number of the unknown seeds for 3D graph would be solved in the less constrained sparse linear system of function. Experimental results demonstrate our RWNBT method achieved a speedup over RW3D while maintaining a high level accuracy.
Regarding the interactive segmentation algorithm, selection of the object and background seeds is considered a critical factor since it influences the overall per-formance of the segmentation method. Fig. 3.8 shows the Dice similarity coefficient for different size by using the defined seeds with only a fixed number. Regardless of the image size, a significant segmentation result can be achieved using our proposed RWNBT method. It confirmed the ability of our method to robustly segment the liver with a high precision result under the weak boundary conditions.
Quantitative and comparative results from applying the RW3D and RWNBT methods for the liver segmentation are presented in Fig. 3.9. In order to intuitively make a comparison between our proposed RWNBT and RW3D methods, it was unreasonable to give only one start slice with the corresponding segmentation re-sult. It was necessary to show different slices for one data corresponding to a point on the curve with 128×86×33 pixels in Fig. 3.8. The red images were segmented liver slices, which were overlaid with the original CT slices. The simulation verifies that the performance of RWNBT was significantly better than the RW3D method for segmenting the liver.
In this research, we applied our proposed method to a large number of liver shapes. Fig. 3.10 compares the accuracy between the RW3D and RWNBT method for another clinical case with a size of 126 ×96×36 pixels, again showing our proposed method gives excellent accuracy.
Moreover, in order to make a comparison with the state-of-the-art interactive segmentation algorithms, we compared the results using Graph Cut algorithm(GC)
Figure 3.8: Comparison of the runtime and accuracy of the classical RW3D (blue) and our proposed method RWNBT (red) for different sized 3D image.
Figure 3.9: Comparison of liver segmentation results with RWNBT method and RW3D method in Case 4.
Figure 3.10: Comparison of liver segmentation results with RWNBT method and RW3D method in Case 6 of Group-I dataset.
Table 3.1: Segmentation accuracy obtained by the state-of-the-art methods for the liver on Group-I dataset.
Average RW3D [8] GC [5] IKM [20] RWNBT
Dice 0.573 0.857 0.894 0.942
VOE 0.404 0.758 0.810 0.890
Runtime (sec) 105.655 1.828 5.236 1.527
[5] and Interactive K-means algorithm (IKM) [20]. Table 3.1 clearly depicts the merits of our method by listing the comparative results with the average of Dice, VOE and Runtime between automated and manual segmentations for all 26 tests CT scans. The accuracy of RWNBT was observed to have significantly higher Dice/VO and lower Runtime than state-of-the-art interactive segmentation meth-ods.To directly demonstrate the performance of our proposed method, in respect to the statistical significance analysis, the p-value was the probability of obtaining a test statistic result that was actually observed. These statistics test demonstrated that our proposed RWNBT approach yields the high precision results with respect to the conventional RW3D method (p < 0.001).
Figure 3.11: Comparison of manual segmentation (blue) and the segmentation results of our method (red) for the Group II dataset (High-resolution). The first row is Case 1 of Group-II dataset. The second row is Case 3 of Group-II dataset.
(a) The seed points on one start slice; (b)-(d) Different slices of the segmented volume; (e) Visualization of the segmented volume.
3.5.4 Multi-Organ Segmentation Results
A. Quantitative Validation of Multi-Organ Segmentation
High-resolution Segmentation To investigate the performance of our pro-posed segmentation method, we applied our propro-posed RWNBT method to the Group II dataset (High-resolution), which were described in previous section. The segmentation results of two typical cases are shown in Fig. 3.11. The results in Fig. 3.11 proved that performing our RWNBT method to segment the liver and spleen can give us the accurate results.
Quantitative evaluation results for liver and spleen segmentation with phase-ART are presented in Fig. 3.12. The accuracy of the liver segmentation is the average Dice’s similarity coefficient of 0.952, the spleen segmentation results in an the average Dice coefficient of 0.950. These results confirmed the ability of our method to simultaneously segment the liver and spleen precisely.
The basic idea of our proposed RWNBT method was based on the high resolu-tion between adjacent slices. Seed points for the current slice were automatically generated according to the prior knowledge from the segmented organs region of the previous slice. As shown in Fig. 3.12, precise results were achieved in our experiments since we used high resolution data.
Low-resolution Segmentation In order to verify the effect of resolutions on our RWNBT method, our proposed RWNBT method was also applied to the Group III dataset (Low-resolution). Two typical cases were shown in Fig. 3.13.
Figure 3.12: The segmentation accuracy for the Group II dataset (High-resolution).
Table 3.2: Effect of resolution on segmentation accuracy.
Dice Liver Spleen
Group II (1.25mm) 0.952±0.015 0.950±0.018 Group III (5.75mm) 0.934±0.035 0.923±0.068
Meanwhile, Fig. 3.14 and Fig. 3.15 give a more clear depiction of the corresponding accuracy results of the Group III dataset. Experiment results demonstrate that our RWNBT method achieved a high precision result under low resolution conditions.
Table 3.2 lists the segmentation accuracy (Dice) between the Group-II dataset (High-resolution) and Group-III dataset (Low-resolution). It indicates that our proposed technique can be performed on the CT scans regardless of the resolution by yielding satisfactory segmentation results. The results proved our RWNBT method is robust to multi-organ segmentation using various resolutions of CT scans.
B. Qualitative Comparison of Multi-Organ Segmentation
To evaluate the effectiveness of the proposed method (RWNBT), RWNBT was compared with the classical Random walks (RW3D) algorithm [30]. For the RWG-MM3D algorithm, the intensity information of organs (Gaussian mixture model) was integrated into the RW3D method. Considering the memory usage demands for applying the RW3D algorithm in the computer, we used the Group-III dataset (Low resolution: 128×128×36 voxels) for comparison of performance.
To assess the potential benefits of our proposed method, quantitative and com-parative results from applying the RW3D and RWNBT methods for the multi-organ segmentation are presented in Fig. 3.14 and Fig. 3.15. The results indicated that our proposed RWNBT method can achieve more accurate segmentation re-sults than the conventional RW3D method. Moreover, it can be seen that there
Figure 3.13: Comparison of the segmentation results of our method with the Group III dataset (Low-resolution). The first row is Case 11 of Group-III dataset. The second row is Case 13 of Group-III dataset. (a) The seed points on one start slice;
(b)-(d) Different slices of the segmented volume.
Figure 3.14: The liver segmentation accuracy for the Group III dataset (Low-resolution).
Figure 3.15: The spleen segmentation accuracy for the Group III dataset (Low-resolution).
are still a lot of false positives in the RWGMM3D method despite using a Gaussian mixture model, because shape knowledge were not used. In order to intuitively make a comparison between our proposed RWNBT and RW3D methods, 2D slices were used for observation about the corresponding segmentation results (Fig. 3.16).
The red ones are segmented organ slice, which were overlaid with the original CT slices. The simulation verifies that the performance of RWNBT was significantly better than the RW3D method for segmenting multiple organs.
Moreover, Table 3.3 summarized the comparative results with the average of Dice and Runtime for the Group-III dataset. The accuracy of RWNBT was ob-served to have significantly higher Dice than the state-of-the-art interactive seg-mentation methods. A significant reduction in runtime values using RWNBT segmentation method compared with those based on RW3D was confirmed. Com-putation time is an important metric for evaluating one segmentation algorithm.
For the classical RW algorithm, the basis of the RW method is a set of large, sparsely occupied linear equations, whose size corresponds to the number of voxels in the 3D medical image. Hence, it is slow when solving 3D image segmentation.
To directly demonstrate the performance of our proposed method, statistical sig-nificance using the p-values was used to define the probability of obtaining a test statistic result that was actually observed. These statistics demonstrated that our proposed RWNBT approach yields the high precision results with respect to the conventional RW3D method (p < 0.001).